Study of bubble structure in N = 20 isotones within relativistic mean-field plus BCS approach

Guided by various theoretical studies and encouraged with recent first experimental evidence of proton density depletion in ³⁴Si, we have applied relativistic mean field plus BCS approach for systematic study of bubble structure in magic nuclei with N = 20 isotones. Our present investigations include single particle energies, deformations, separation energies as well as neutron and proton densities etc. It is found that proton sd shells (1d_5/2,2s_1/2,1d_3/2) in N = 20 isotones play very important role in the formation of bubble structure. The unoccupied 2s_1/2 state gives rise to bubble since this 2s_1/2 state does not have any centrifugal barrier, therefore for Z = 8 - 14 in the isotonic chain radial distributions of such state is found with peak in the interior of the nucleus with corresponding wave functions extending into the surface region. Consequently, in these nuclei with unoccupied s-state the central density found depleted as compared to the nucleus wherein this state is fully occupied. It is important to note here that in these nuclei depletion in proton density for ³⁴Si is found with most significance which is in accord with the recent experiment. Moving further for higher Z value, Z = 16 and Z = 18 the 2s_1/2 state remains semi-occupied and contributing partially in the depletion of central density resulting semi-bubble structure for Z = 16 and 18. For Z≥20, 2s_1/2 state get fully occupied and no sign of bubble structures are seen for higher isotones